2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157442In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of Martel and Merle (arXiv:0706.1174v2). As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.Submitted for publication on December 26, 2007Analysis of PDEs35Q53, 35Q51, 35B40text